Secure the fabric along all of the straight edges to begin upholstering your item. Leave the corners undone so that the square corners of the fabric are sticking out all around.
Choose one corner at which to begin. Start at one end and make small pleats in the fabric, pressing and holding them down against the underside of the piece. Stop when you reach the center of the corner and secure the pleated edge to the underside with a staple or upholstery nail.
Begin pleating again from the opposite side of the same corner, stopping when you reach the center and securing the fabric as you did before. There is now a “lip” of fabric in the center. Pull this piece down tightly and create pleats at either edge until the fabric is smooth wherever it will be visible; secure the fabric to the underside and finish the other three corners.